Macroeconomics, Fall 2009 CHAPTER THREE National Income: Where it Comes From and Where it Goes

In this chapter you will learn: what determines the economy’s total output/income how the prices of the factors of production are determined how total income is distributed what determines the demand for goods and services how equilibrium in the goods market is achieved

Outline of model A closed economy(No Net Export), market-clearing model(Prices ensure D=S) Supply side factor markets (supply, demand, price) determination of output/income Demand side determinants of C, I, and G Equilibrium goods market loanable funds market It’s useful for students to keep in mind the “big picture” as they learn the individual components of the model in the following slides.

Factors of production K = capital, tools, machines, and structures used in production L = labor, the physical and mental efforts of workers In the simple model of this chapter, we think of capital as plant & equipment. In the real world, capital also includes inventories and residential housing, as discussed in Chapter 2. Students may have learned in their principles course that “land” or “land and natural resources” is an additional factor of production. In macro, we mainly focus on labor and capital, though. So, to keep our model simple, we usually omit land as a factor of production, as we can learn much of what we need to know about macroeconomics without the factor of production land.

The production function denoted Y = F (K, L) shows how much output (Y ) the economy can produce from K units of capital and L units of labor. reflects the economy’s level of technology. exhibits constant returns to scale (CRS). What is CRS? (Read pages 55-58 including technical note)

Assumptions of the model Technology is fixed. The economy’s supplies of capital and labor are fixed at Emphasize that “K” and “L” (without bars on top) are variables - they can take on various magnitudes. On the other hand, “Kbar” and “Lbar” are specific values of these variables. Hence, “K = Kbar” means that the variable K equals the specific amount Kbar. Regarding the assumptions: In chapters 7 and 8 (Economic Growth I and II), we will relax these assumptions: K and L will grow in response to investment and population growth, respectively, and the level of technology will increase over time.

Determining GDP Output is determined by the fixed factor supplies and the fixed state of technology: Again, emphasize that “F(Kbar,Lbar)” means we are evaluating the function at a particular combination of capital and labor. The resulting value of output is called “Ybar”.

The distribution of national income determined by factor prices, the prices per unit that firms pay for the factors of production. The wage is the price of L , the rental rate is the price of K. Recall from chapter 2: the value of output equals the value of income. The income is paid to the workers, capital owners, land owners, and so forth. We now explore a simple theory of income distribution.

Notation W = nominal wage R = nominal rental rate P = price of output W /P = real wage (measured in units of output) R /P = real rental rate Recall the difference between nominal and real variables. The nominal wage & rental rate are measured in currency units. The real wage is measured in units of output. To see this, suppose W = $10/hour and P = $2 per unit of output. Then, W/P = ($10/hour) / ($2/unit of output) = 5 units of output per hour of work. It’s true, the firm is paying the workers in money units, not in units of output. But, the real wage is the purchasing power of the wage - the amount of stuff that workers can buy with their wage.

How factor prices are determined Factor prices are determined by supply and demand in factor markets (LABOR AND CAPITAL). Recall: Supply of each factor (labor or capital) is fixed. What about demand (of labor or Capital)? Since the distribution of income depends on factor prices, we need to see how factor prices are determined. Each factor’s price is determined by supply and demand in a market for that factor. For instance, supply and demand for labor determine the wage.

Demand for labor Assume markets are competitive: each firm takes W, R, and P as given Basic idea: A firm hires each unit of labor if the cost does not exceed the benefit. cost = real wage benefit = marginal product of labor

Marginal product of labor (MPL) def: The extra output the firm can produce using an additional unit of labor (holding other inputs fixed): MPL = F (K, L +1) – F (K, L)

Exercise: compute & graph MPL L Y MPL 0 0 n.a. 1 10 ? 2 19 ? 3 27 8 4 34 ? 5 40 ? 6 45 ? 7 49 ? 8 52 ? 9 54 ? 10 55 ? Determine MPL at each value of L Graph the production function Graph the MPL curve with MPL on the vertical axis and L on the horizontal axis This exercise is pretty basic review. It’s good for students who have not had principles of economics in a few years, and students whose graphing skills could benefit from some remedial attention. Many instructors could probably “hide” or omit this and the next slide from their presentations.

answers:

The MPL and the production function Y output 1 MPL As more labor is added, MPL  1 MPL (Figure 3-3 on p.49) It’s straightforward to see that the MPL = the prod function’s slope: The definition of the slope of a curve is the amount the curve rises when you move one unit to the right. On this graph, moving one unit to the right simply means using one additional unit of labor. The amount the curve rises is the amount by which output increases: the MPL. Slope of the production function equals MPL MPL 1 L labor

Diminishing marginal returns As a factor input is increased, its marginal product falls (other things equal). Intuition: L while holding K fixed  fewer machines per worker lower productivity EXAMPLE 1 PIZZA machine and three workers = 100 PIZAS in one hour 1 PIZZA machine and hundred workers = ? PIZZAS in one hour Many production functions have this property. This slide introduces some short-hand notation that will appear throughout the PowerPoint presentations of the remaining chapters: The up and down arrows mean increase and decrease, respectively. The symbol “” means “causes” or “leads to.” Hence, the text after “Intuition” should be read as follows: “An increase in labor while holding capital fixed causes there to be fewer machines per worker, which causes lower productivity.” Many instructors use this type of short-hand (or something very similar), and it’s much easier and quicker for students to write down in their notes.

MPL and the demand for labor Each firm hires labor up to the point where MPL = W/P Units of output Units of labor, L MPL, Labor demand Each firm hires labor up to the point where P*MPL = W or the contribution of labor to output in terms of value is the same as the cost of labor or the wage Real wage Quantity of labor demanded It’s easy to see that the MPL curve is the firm’s L demand curve. Let L* be the value of L such that MPL = W/P. Suppose L < L*. Then, benefit of hiring one more worker (MPL) exceeds cost (W/P), so firm can increase profits by hiring one more worker. Instead, suppose L > L*. Then, the benefit of the last worker hired (MPL) is less than the cost (W/P), so firm should reduce labor to increase its profits. When L = L*, then firm cannot increase its profits either by raising or lowering L. Hence, firm hires L to the point where MPL = W/P. This establishes that the MPL curve is the firm’s labor demand curve.

Question: Why is the MPL curve the Labor Demand Curve It’s easy to see that the MPL curve is the firm’s L demand curve. Let L* be the value of L such that MPL = W/P. Suppose L < L*. Then, benefit of hiring one more worker (MPL) exceeds cost (W/P), so firm can increase profits by hiring one more worker. Instead, suppose L > L*. Then, the benefit of the last worker hired (MPL) is less than the cost (W/P), so firm should reduce labor to increase its profits. When L = L*, then firm cannot increase its profits either by raising or lowering L. Hence, firm hires L to the point where MPL = W/P. This establishes that the MPL curve is the firm’s labor demand curve. Recall the definition of the demand curve: Tells us how many units will be demanded at a Particular price. It’s easy to see that the MPL curve is the firm’s L demand curve. Let L* be the value of L such that MPL = W/P. Suppose L < L*. Then, benefit of hiring one more worker (MPL) exceeds cost (W/P), so firm can increase profits by hiring one more worker. Instead, suppose L > L*. Then, the benefit of the last worker hired (MPL) is less than the cost (W/P), so firm should reduce labor to increase its profits. When L = L*, then firm cannot increase its profits either by raising or lowering L. Hence, firm hires L to the point where MPL = W/P. This establishes that the MPL curve is the firm’s labor demand curve.

The equilibrium real wage Units of output Units of labor, L Labor supply MPL, Labor demand equilibrium real wage The labor supply curve is vertical: We are assuming that the economy has a fixed quantity of labor, Lbar, regardless of whether the real wage is high or low. Combining this labor supply curve with the demand curve we’ve developed in previous slides shows how the real wage is determined. The real wage adjusts to equate labor demand with supply.

Determining the rental rate We have just seen that MPL = W/P The same logic shows that MPK = R/P : diminishing returns to capital: MPK  as K  The MPK curve is the firm’s demand curve for renting capital. Firms maximize profits by choosing K such that MPK = R/P . In our model, it’s easiest to think of firms renting capital from households (the owners of all factors of production). R/P is the real cost of renting a unit of K for one period of time. In the real world, of course, many firms own some of their capital. But, for such a firm, the market rental rate is the opportunity cost of using its own capital instead of renting it to another firm. Hence, R/P is the relevant “price” in firms’ capital demand decisions, whether firms own their capital or rent it.

The equilibrium real rental rate Units of output Units of capital, K Supply of capital The real rental rate adjusts to equate demand for capital with supply. MPK, demand for capital equilibrium R/P The previous slide used the same logic behind the labor demand curve to assert that the capital demand curve is the same as the downward-sloping MPK curve. The supply of capital is fixed (by assumption), so the supply curve is vertical. The real rental rate (R/P) is determined by the intersection of the two curves.

The Neoclassical Theory of Distribution states that each factor input is paid its marginal product accepted by most economists

How income is distributed: total labor income = total capital income = If production function has constant returns to scale, then national income labor income capital income

Outline of model A closed economy, market-clearing model Supply side factor markets (supply, demand, price) determination of output/income Demand side determinants of C, I, and G Equilibrium goods market loanable funds market DONE  DONE  Next 

Demand for goods & services Components of aggregate demand: C = consumer demand for g & s I = demand for investment goods G = government demand for g & s (closed economy: no NX ) “g & s” is short for “goods & services”

Consumption, C def: disposable income is total income minus total taxes: Y – T Consumption function: C = C (Y – T ) Shows that (Y – T )  C def: The marginal propensity to consume is the increase in C caused by a one-unit increase in disposable income. Again, we are using the short-hand notation that will appear throughout the remaining PowerPoints: X  Y means “an increase in X causes a decrease in Y.”

The consumption function Y – T C (Y –T ) The slope of the consumption function is the MPC. MPC 1

Investment, I The investment function is I = I (r ), where r denotes the real interest rate, the nominal interest rate corrected for inflation. The real interest rate is  the cost of borrowing  the opportunity cost of using one’s own funds to finance investment spending. So, r  I

The investment function r I Spending on investment goods is a downward-sloping function of the real interest rate I (r )

Government spending, G G includes government spending on goods and services. G excludes transfer payments Assume government spending and total taxes are exogenous: It might be useful to remind students of the meaning of the terms “exogenous” and “transfer payments.”

The market for goods & services The real interest rate adjusts to equate demand with supply. Note the only variable in the equilibrium condition that doesn’t have a “bar” over it is the real interest rate. It is the only varying variable. This r links the financial market to the goods market. This same r establishes equilibruimm in both the goods and financial markets. Note the only variable in the equilibrium condition that doesn’t have a “bar” over it is the real interest rate. When the full slide is showing, before you advance to the next one, you might want to note that the interest rate is important in financial markets as well, so we will next develop a simple model of the financial system.

The loanable funds market A simple supply-demand model of the financial system. One asset: “loanable funds” demand for funds: investment supply of funds: saving “price” of funds: real interest rate

Demand for funds: Investment The demand for loanable funds… comes from investment: Firms borrow to finance spending on plant & equipment, new office buildings, etc. Consumers borrow to buy new houses. depends negatively on r , the “price” of loanable funds (the cost of borrowing).

Loanable funds demand curve I The investment curve is also the demand curve for loanable funds. I (r )

Supply of funds: Saving The supply of loanable funds comes from saving: Households use their saving to make bank deposits, purchase bonds and other assets. These funds become available to firms to borrow to finance investment spending. The government may also contribute to saving if it does not spend all of the tax revenue it receives.

Types of saving private saving = (Y –T ) – C public saving = T – G national saving, S = private saving + public saving = (Y –T ) – C + T – G = Y – C – G After showing definition of private saving, - give the interpretation of the equation: private saving is disposable income minus consumption spending - explain why private saving is part of the supply of loanable funds: Suppose a person earns $50,000/year, pays $10,000 in taxes, and spends $35,000 on goods and services. There’s $5000 remaining. What happens to that $5000? The person might use it to buy stocks or bonds, or she might put it in her savings account or money market deposit account. In all of these cases, this $5000 becomes part of the supply of loanable funds in the financial system. After displaying public saving, explain the equation’s interpretation: public saving is tax revenue minus government spending. Notice the analogy to private saving – both concepts represent income less spending: for the private household, income is (Y-T) and spending is C. For the government, income is T and spending is G.

Loanable funds supply curve S, I National saving does not depend on r, so the supply curve is vertical.

Loanable funds market equilibrium S, I I (r ) Equilibrium real interest rate Equilibrium level of investment

The special role of r r adjusts to equilibrate the goods market and the loanable funds market simultaneously: If Loanable funds ( L.F.) market in equilibrium, then Y – C – G = I (National S = Inv) Add (C +G ) to both sides to get Y = C + I + G (goods market eq’m) Thus, This slide establishes that we can use the loanable funds supply/demand diagram to see how the interest rate that clears the goods market is determined. Explain that the symbol  means each one implies the other. The thing on the left implies the thing on the right, and vice versa. More short-hand: “eq’m” is short for “equilibrium” and “LF” for “loanable funds.” Eq’m in L.F. market Eq’m in goods market

Mastering the loanable funds model 1. Things that shift the saving curve public saving fiscal policy: changes in G or T private saving preferences tax laws that affect saving 401(k) IRA Continuing from the previous slide, let’s look at all the things that affect the S curve. Then, we will pick one of those things and use the model to analyze its effects on the endogenous variables. Then, we’ll do the same for the I curve. In the United States of America, a 401(k) plan allows a worker to save for retirement and have the savings invested while deferring current income taxes on the saved money and earnings until withdrawal. The employee elects to have a portion of his or her wages\paid directly, or "deferred," into his or her 401(k) account. This deferment is also known as a "contribution". 401(k) plans are mainly employer sponsored plans An Individual Retirement Arrangement (or IRA) is a retirement plan account that provides some tax advantages for retirement savings in the US

HOME WORK (NOT GRADED) Draw the diagram for the loanable funds model. Suppose the tax laws are altered to provide more incentives for private saving. What happens to the interest rate and investment? (Assume that T doesn’t change) Students may be confused because we are (somehow) changing taxes, but assuming T is unchanged. Taxes have different effects. The total amount of taxes (T ) affects disposable income. But even if we hold total taxes constant, a change in the structure or composition of taxes can have effects. In this problem, we’re holding total taxes constant, so disposable income does not change, but we are changing the composition of taxes to give consumers an incentive to increase their saving.

Mastering the loanable funds model 2. Things that shift the investment curve certain technological innovations to take advantage of the innovation, firms must buy new investment goods tax laws that affect investment investment tax credit

An increase in investment demand S, I I2 An increase in desired investment… I1 …raises the interest rate. r2 r1 But the equilibrium level of investment cannot increase because the supply of loanable funds is fixed.

Saving and the interest rate Why might saving depend on r ? How would the results of an increase in investment demand be different? Would r rise as much? Would the equilibrium value of I change?

An increase in investment demand when saving depends on the interest rate [the supply curve is sloping up] This is Figure 3-11 from page 65 of the text. See accompanying discussion.

Chapter summary Total output is determined by how much capital and labor the economy has the level of technology Competitive firms hire each factor until its marginal product equals its price. If the production function has constant returns to scale, then labor income plus capital income equals total income (output).

Chapter summary The economy’s output is used for consumption (which depends on disposable income) investment (depends on the real interest rate) government spending (exogenous) The real interest rate adjusts to equate the demand for and supply of goods and services loanable funds

Chapter summary A decrease in national saving causes the interest rate to rise and investment to fall. An increase in investment demand causes the interest rate to rise, but does not affect the equilibrium level of investment if the supply of loanable funds is fixed.

Notation:  = change in a variable For any variable X, X = “the change in X ”  is the Greek (uppercase) letter Delta Examples: If L = 1 and K = 0, then Y = MPL. More generally, if K = 0, then (YT ) = Y  T , so C = MPC  (Y  T ) = MPC Y  MPC T